A rigorous coupled wave analysis (RCWA) and similar algorithms have been widely used for the study and design of diffraction structures. In the RCWA approach, the profiles of periodic structures of a certain target structure are approximated by a given number of sufficiently thin planar grating slabs.
Specifically, RCWA involves three main operations, namely, the Fourier expansion of the field inside the grating, calculation of the eigenvalues and eigenvectors of a constant coefficient matrix that characterizes the diffracted signal, and solution of a linear system deduced from the boundary matching conditions. RCWA divides the problem into three distinct spatial regions: (1) the ambient region supporting the incident plane wave field and a summation over all reflected diffracted orders, (2) the grating structure and underlying non-patterned layers in which the wave field is treated as a superposition of modes associated with each diffracted order, and (3) the substrate containing the transmitted wave field.
In the establishment of RCWA and similar processes, a Fourier harmonic order is required for computation of spectral information for periodic structures of a larger target structure. However, the determination of an appropriate Fourier harmonic order for such computation can be difficult and require large computational costs.